Page 45 - NUMINO Challenge_C1

5 A Winning Strategy Using Symmetry

Basic Concepts Placing Coins on a Round Table

In this game, two players take turns placing coins on a
round table, making sure that the coins do not overlap.
The player who cannot find any more space to place
his coin loses.

Winning strategy

1. Start first and place the coin at the center of the table.
2. From the next turn, place the coin so that it has point

symmetry with respect to the opponent s coin.

Example Two people sit facing each other at a round table and play a game
according the rules below. Who has the advantage: the first player
or the second player?

Rules

1. Each player places down one coin, of the same size, per turn.
2. Coins cannot overlap.
3. The player who places down the last coin wins.

Class Notes

Start (first, second) and set the point of symmetry by placing your coin at the center
of the round table.
When your opponent places a coin, place your coin such that it has point symmetry
with respect to your opponent’ s coin.
Continue in this way and your opponent will run out of places to place his/her coin.

In order to always win, you must start (first, second) and place your coin at the
of the round table.

42 NUMINO Challenge C1